Several things could be at play here. As the previous poster suggested, you can do a hard reset. Hold down the power button and home button at the same time. This will force the phone to perform a hard reset.
If that does not work, then we will want to do a full restore on the iPhone. MAKE SURE ALL OF YOUR DATA IS BACKED-UP TO iTUNES BEFORE DOING THIS STEP.
Turn the phone off. Now, hold down the power button and home button until the Apple logo appears. Once it appears let go of just the power button (still holding down the home button). This will force the iPhone into DFU mode and the display will show the icon for iTunes and a USB cable. Now connect your iPhone to iTunes and do a complete restore.
If that does not resolve it, then it sounds like the LCD may have gone bad. We would recommend replacing the LCD as the next step to see if that resolves the no image issue. If you still have no image after replacing the LCD, then it is likely that the video component on the motherboard has gone bad. The phone likely can not be fixed.
We see these 'no image' issues in our repair shop every day and these would be the basic troubleshooting steps that you can do at home to resolve the issue.